Power system model parameter conditioning tool

ABSTRACT

A power system model parameter conditioning tool including a server control processor in communication with phasor measurement unit monitored data records of multiple disturbance events, a model calibration unit providing event screening, power system model simulation, and simultaneous tuning of model parameters. The model calibration performing a simulation using default model parameters, the processor comparing the simulation results to the monitored data. If the prediction is within threshold, then terminating conditioning; else performing parameter identifiability analysis to determine differing effects of various model parameters on power system model accuracy, selecting a parameter set causing a degradation in power system model prediction, and updating the default model parameters corresponding to members of the parameter set with values selected to reduce the degradation. A method and a non-transitory computer readable medium are also disclosed.

GOVERNMENT SUPPORT

Made using government support provided by the U.S. Department of Energyunder Contract No. DE-OE0000858.

BACKGROUND

Power system models are useful in providing critical analysis of powersystem stability. One conventional approach to the validation and/orcalibration of a power system model is to disconnect the power systemcomponent of interest from the electric distribution grid for atemporary period. Disconnection of a power system component such as apower plant reduces the ability of the electrical distribution grid toprovide sufficient power to meet demand in the most cost effectivemanner.

Another conventional approach to validate and/or calibrate a powersystem model is to install one or more phasor measurement units (PMUs)into the electrical distribution grid at remote measurement points. ThePMUs can measure characteristics of the electrical wave(s) present onthe grid at these remote points. The captured measurements can be usedto validate and/or calibrate the power system component model, withoutdisconnecting the component from the grid. However under thisconventional approach, the model calibration results are only valid fora specific disturbance. There is no guarantee that for a subsequentdisturbance the parameter values tuned using a previous disturbance arestill valid. Moreover, the parameter identifiability studies areconducted around the default parameter values. A highly localizedidentifiability study can affect the performance of thevalidation/calibration algorithm used to tune the component of interest.

What is missing from the art is a validation/calibration algorithm totune power system models, which leverages actual PMU measurement data toimprove the model for multiple possible disturbances without the need todisconnect the power system component itself from the electricaldistribution grid to perform the model calibration.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a system that includes a power system model parameterconditioning tool in accordance with embodiments;

FIG. 2 depicts a process for power system model parameter conditioningin accordance with embodiments;

FIG. 3 depicts a spiral graph illustrating the parameter sensitivity ofa power system model's prediction in accordance with embodiments;

FIG. 4 depicts a spiral graph illustrating the parameter sensitivity ofa power system model's active power prediction in accordance withembodiments; and

FIG. 5 depicts a spiral graph illustrating the parameter sensitivity ofa power system model's reactive power prediction in accordance withembodiments.

DETAILED DESCRIPTION

Embodying systems and methods provide a power system model parameterconditioning tool for disturbance-based model validation and orcalibration. This conditioning tool can improve the accuracy of a powersystem model for various types of dynamic devices used as powergeneration systems (i.e. generation plants, renewable energy sources,control devices, dynamic loads, etc.). In accordance with embodiments,high-fidelity disturbance measurement data obtained from PMUs formultiple disturbances can be leveraged to improve the power system modelso that mandated grid reliability requirements can be met.

In accordance with embodiments, a parameter conditioning tool performsanalysis using PMU data from multiple disturbances. This conditioninganalysis can identify the magnitude and dependency of device parametersensitivities in a power system model. From the analysis, a set of powersystem model parameters impacted by one selected disturbance, or more,is passed to a model calibration algorithm. The set of parameters caninclude those model parameters that are most impacted by the particularselected disturbance(s) (i.e., causing the greatest degradation in powersystem model prediction performance). In accordance with embodiments, aparametric sensitivity study can be conducted for differing types ofdisturbance to identify which parameters should be included in the set.

An embodying model calibration algorithm tunes these passed parametersof the power system model to make the outputs generated by the modelmore closely match the signals collected by the PMUs for the selecteddisturbances. In some implementations the generated outputs can be, forexample, real and reactive power outputs. In accordance withembodiments, the parameter tuning considers the effect of multipledisturbances to arrive at a global model validation/calibration to bestfit a variety of disturbances. In accordance with embodiments, acalibration step can tune parameters for multiple disturbancessimultaneously.

Embodying approaches can account for non-linearity in the power systemmodel; account for multiple differing disturbance events; calibrationresults can be localized around assumed default parameter values.Physical constraints of parameters are enforced during modelcalibration, and an embodying calibration algorithm avoids tuning modelparameters that might already be set at their true (e.g., optimal)values.

FIG. 1 depicts system 100 that includes power system model parameterconditioning tool 110 in accordance with embodiments. An embodyingparameter conditioning tool 120 can include server 130 in communicationwith data store 140.

Server 130 can include control processor 131 that communicates withother components of the parameter conditioning tool. Control processor131 accesses computer executable instructions 141, which in someimplementations can be stored in data store 140. The server controlprocessor 131 can support embodying power system model parameterconditioning for disturbance-based model validation and or calibrationby executing executable instructions 141. Dedicated hardware, softwaremodules, and/or firmware can implement embodying approaches disclosedherein.

Server 130 van be in communication with data store 140 directly and/oracross electronic communication network 118. The electroniccommunication network can be, can comprise, or can be part of, a privateinternet protocol (IP) network, the Internet, an integrated servicesdigital network (ISDN), frame relay connections, a modem connected to aphone line, a public switched telephone network (PSTN), a public orprivate data network, a local area network (LAN), a metropolitan areanetwork (MAN), a wide area network (WAN), a wireline or wirelessnetwork, a local, regional, or global communication network, anenterprise intranet, any combination of the preceding, and/or any othersuitable communication means. It should be recognized that techniquesand systems disclosed herein are not limited by the nature of network118.

A power system can include power generation system 110, which provideselectrical power to electrical power distribution grid 112. PMU 115 canbe coupled to the electrical power distribution grid to monitor signalcharacteristics (e.g., voltage (V), frequency (F), active reactive power(P), and nonactive reactive power (Q)). Data obtained by PMU 115 can beprovided to parameter conditioning tool 120 across electroniccommunication network 118. This data can be stored in data records PMUmonitored data 143. It should be readily understood that a power systemis not limited to a single power generation system; that an electricalpower grid can be a vast, interconnected network of multiple producers(power generation systems), transmission lines, substations,transformers, and loads (power consumers); and that multiple PMUs can becoupled to the power grid at a multiple locations.

Under conventional approaches, a power system model is tuned(“calibrated”) for one event (e.g., treating each disturbance eventseparately). This conventional approach results in severely limitingthat model's performance to satisfactorily predict a power system'sperformance in response to a subsequent event. Because embodyingapproaches simultaneously perform power system parameter tuning acrossmultiple events, these system parameters can be provided to a powersystem model. By incorporating the tuned parameters into the powersystem model, the model can more accurately predict power systemperformance than conventionally-calibrated (“tuned”) models.

In accordance with embodiments, the parameter conditioning toolgenerates trajectory sensitivity matrices for all the selecteddisturbances. These matrices are generated by perturbing each modelparameter and feeding the perturbed parameter values to modelcalibration unit 133. Depending on the number of disturbances beingconsidered, model calibration algorithm 144 can follow two options.

If the number of disturbances is large enough that the union of nullspaces of the sensitivity matrices of all the disturbances has a rankhigher than the parameter number, an embodying model calibrationalgorithm can solve an optimization problem to find a solution that hasthe minimum total distance to all the null spaces. The solution reflectsthe parameter set that has dependencies in one or more of thesedisturbances. Therefore, such a solution gives a comprehensiveidentifiability ranking of parameters across disturbances.

If the number of disturbances is small, a second option can beimplemented by model calibration algorithm 144. This second optionevaluates the identifiability of parameters for each disturbance, thencalculates the average identifiability ranking across disturbances.Since the sensitivity studies are conducted at the parameters' defaultvalues, the parameter conditioning tool can also perform a globalsensitivity consistency study when the parameters' values deviate faraway from their default values. Such study can portray the geometry ofthe parameter sensitivity in the entire parameter space.

Since different events may have different characteristics, theconventional identifiability analysis corresponding to each single eventmay not be applicable to other events. For example, a set ofmost-identifiable parameters for event A may not be identifiable forevent B. Then, for a single event calibration, the value of this set ofparameters is only tuned by a conventional approach to make the outputmatch event A's measurement data. But when the tuned parameter valuesare used to simulate event B, there could still be discrepancy betweensimulation output from the power system model and measurement data fromPMUs.

In accordance with embodiments, because there is availability ofmeasurement data from multiple events, a comprehensive identifiabilitystudy across multiple events can be performed. This comprehensive studycan provide a most-identifiable parameter set for the simultaneouscalibration of multiple disturbances. In accordance with embodiments,this parameter set can be used to tune power system model 146 to bettermatch (when compared to conventionally-tuned power system models) themeasurement data of multiple events simultaneously.

When a quantity of N events is considered, applying singular-valuedecomposition (SVD) analysis to the sensitivity trajectory matricesresults in a quantity of null spaces equal to the value of N. The nullspace for one event also can be interpreted as a system of homogeneousalgebraic equations with parameter sensitivities being the unknowns.Since the null space from one event has a rank lower than the number ofparameters, the number of equations is less than the number of unknowns.

Considering more events is equivalent to adding more equations to thesystem. After the event number N exceeds a certain value (also thecharacteristic of events should be diverse), the system would have moreequations than unknowns. In implementation, the numerical rank should begreater than the number of unknowns. The solution that minimizes thedifference between the left and right hand of the equation systemrepresents the comprehensive sensitivity magnitude of all parametersacross all the considered events. For sensitivity dependency, accountingfor the null spaces of all considered events, a comprehensive dependencyindex can also be calculated.

In accordance with embodiments, if the number of events is not largeenough to construct a null space with higher rank than the number ofparameters, the identifiability for each single event is analyzed, andthen the average identifiability can be uses as the identifiabilityacross all events.

In accordance with embodiments, model calibration algorithm 144 canimplement Algorithm I to perform a sensitivity dependency calculationusing null space of the trajectory sensitivity matrix to calculatesensitivity dependency. The dependency index can be defined by countingthe large elements in the right singular vectors in null space.

ALGORITHM I procedure DEPENDENCY (NullSpace) M ← number of parameters N← number of right singular vectors in null space  for j ← 1, M do  D_(j)← 0  end for for i ← 1, N do(Search for direct dependencies)  for j ← 1,M do for k ← 1, M do if NullSpace(k, i) ≥ threshold then D_(j) ← D_(j) ∪k end if end for end for end for for j ← 1, M do  L(j) ← | D_(j) | endfor k ← 1 for j ← 1, M do (Search for indirect dependencies) while k ≤L(j) do  D_(indirect) ← D_(j) \ D_(Dj(k))  if D_(indirect) ≠ 0 then D_(j) ← D_(j) ∪ D_(indirect)  L(j) ← L(j) + | D_(indirect) |  end if  k← k + 1 end while end for end procedure

FIG. 2 depicts process 200 for power system model parameter conditioningin accordance with embodiments. Disturbance data monitored by one ormore PMUs 115 coupled to electrical power distribution grid 112 isreceived, step 205. The disturbance data can include voltage, frequency,active and nonactive reactive power measurements from one or more pointsof interest on the electrical power grid. This data can be stored in PMUmonitored data 143.

A playback simulation using default model parameters can be performed,step 210. These default parameters can be the current parametersincorporated in the power system model. The current parameters can bestored in model parameter record 145. The simulation can be done bymodel calibration unit 133, which can use a power system simulationengine such as GE PSLF, Powertech TSAT to perform a real-time powersystem simulation scenario.

In accordance with embodiments, the model calibration unit can implementmodel calibration with three functionalities. The first functionality isan event screening tool to select characteristics of disturbance eventfrom a library of recorded event data. This functionality can simulatethe power system responses when the power system is subjected todifferent disturbances. The second functionality is a preconditioningtool for the parameter identifiability study. When implementing thisfunctionality, model calibration unit 133 can simulate the response(s)of a power system model. The third functionality is a tool forsimultaneous tuning of models using an augmented event comprised ofmultiple events.

In accordance with embodiments, event screening can be implementedduring the simulation to provide computational efficiency. If hundredsof events are stitched together and fed into the calibration algorithmunselectively, the algorithm may not be able to converge. To maintainthe number of events manageable and still keep an acceptablerepresentation of all the events, a screening procedure needs to beperformed to select the most characteristic events among all. Dependingon the type of events, the measurement data could have differentcharacteristics. For example, if an event is a local oscillation, theoscillation frequency in the measurement data would be much faster thanan inter-area oscillation event. In some implementations, a K-medoidsclustering algorithm can be utilized to group events with similarcharacteristic together, thus reducing the number of events to becalibrated.

The results of the simulated default model performance can be compared,step 215, to actual disturbance data measured on the power system. Ifthe default model performance is within (e.g., equal to or less than) apredetermined threshold of accuracy (e.g., specified by, for example,power system operators/designers, etc.), Process 200 can end parameterconditioning (step 222), and wait for disturbance data from a subsequentevent (step 225).

If the default model performance is outside of the predeterminedthreshold, a parameter identifiability algorithm is performed, step 230.In accordance with embodiments, the parameter identifiability analysiscan determine the differing effects that various parameters can have onpower system model 146. In some implementations, each parameter canrepresent a factor/coefficient in a term of a polynomial expressionrepresenting the power system model. To decide which parameters of thepower system model are the best choice to tune, a parameter sensitivitystudy is usually performed before model calibration. The sensitivitystudy can vary the value of the parameter, compare the power systemmodel result to monitored data, and then determine the perturbation'smagnitude caused by the variation in parameter value.

To calculate the model's sensitivity to each parameter, playbacksimulation is conducted with the value of that parameter perturbedupward and downward. The difference in the model's performance (i.e.,when compared to the measured disturbance data) between the up, and thedown perturbation yields the trajectory sensitivity matrix.

In accordance with embodiments, the parameter identifiability analysisaddresses two aspects: (a) magnitude of sensitivity of output toparameter change; and (b) dependencies among different parametersensitivities. For example, if the sensitivity magnitude of a particularparameter is low, the parameter would appear in a row being close tozero in the parameter estimation problem's Jacobian matrix. Also, ifsome of the parameter sensitivities have dependencies, it reflects thatthere is a linear dependence among the corresponding rows of theJacobian. Both these scenarios lead to singularity of the Jacobianmatrix, making the estimation problem infeasible. Therefore it iscritical to down select parameters which are highly sensitive as well asresult in no dependencies among parameter sensitivities.

In accordance with embodiments, the identifiability analysis canconsider one disturbance event at a time as well as consider multipledisturbance events simultaneously. For a single event, the trajectorysensitivity matrix contains the information of the magnitude anddependency of parameter sensitivity. Singular value decomposition (SVD)is a useful tool for extracting such information. Let A be the Nt-by-Nptrajectory sensitivity matrix, where Nt is the number of time samples,Np is the number of parameters. The SVD of A is,A=USV^(T)  (EQ. 1)

where the Nt-by-Nt matrix U's columns are the left singular vectorsu_(i)'s (i=1 . . . Nt) of A; the Nt-by-Np matrix S's upperleft diagonalelements are the singular values σi's (i=1 . . . Np) of A; and theNp-by-Np matrix V's columns are the right singular vectors vi's (i=1 . .. Np) of A.

After applying SVD to the trajectory sensitivity matrix A, the magnitudeof the parameter sensitivities can be calculated asM_(sen)=Σ_(i=1) ^(N) ^(p) σ_(i) ²v_(i) ²  (EQ. 2)

The dependency of parameter sensitivities can also be calculated fromthe result of SVD. The dependency of parameter sensitivities iscontained in the right singular vectors corresponding to zero singularvalues (i.e., null space). For each column of the null space, if thereare more than one element larger than a predefined threshold, theparameter sensitivities corresponding to those elements have dependency.This dependency can be explained by the definition of null space. Everyright singular vector in the null space represents a zero-mode, thevalue of elements in that right singular vector indicate thecontribution of parameter sensitivities to that zero mode. If there aremultiple large elements, they contribute to the zero mode by offsettingeach other.

Most algorithmic approaches to model calibration rely, one way oranother, on the sensitivity of the system response to the parameter. Ifindependent perturbations to a set of parameters have low or dependentresponse, a conventional algorithmic model calibration approach can failto identify such a parameter set uniquely. Furthermore, having such asubset of parameters in the estimation set typically leads to numericalissues in calibration algorithms. Because the number of functionevaluations (simulation runs) is proportional to the number ofparameters being estimated, inclusion of such “unidentifiable”parameters leads to unnecessary increase in computation time inconventional approaches. In accordance with embodiments, suchdependencies are identified and isolated before entering the calibrationstage of the embodying model calibration algorithm. This identificationand isolation implemented by disclosed embodiments is an improvementover conventional approaches, and is the rationale for the disclosedtwo-stage approach: identifiability analysis followed by modelcalibration.

Returning to Process 200, after the parameter identifiability at step230, model calibration is performed (step 235). The model calibrationcan use unscented Kalman filter (UKF) to capture nonlinearity in thesystem, and implement optimization-based parameter estimation. In theUKF the parameter identification problem is posed as an estimationproblem, where the uncertain states to be estimated are the parametersof the system. The observation model of the model-based estimationscheme includes the power system model and the tracked outputs. Foroptimization based estimation the parameter identification problem isposed as an optimization problem, where the decision variables of theoptimization problem are the parameters of the power system to beestimated. An optimization problem objective function can include powersystem model outputs and their distance (e.g., 2-norm) to the observedresponse (from PMU measurements).

The parameter values applied in power system model 146 can be updated,step 240. The updated parameter values can be stored in model parameterrecord 145. By applying these conditioned parameter values, the powersystem model can provide more accurate response predictions of a powersystem reaction to disturbance events. After the model parameters areapplied, parameter conditioning is complete (step 222) for theparticular set of monitored PMU data. A report of estimated parametervalue(s), confidence metrics, and model error response vs. measured datacan be generated/displayed. In accordance with embodiments, theparameter condition tool can automatically analyze parametersensitivities and dependencies to identify a selection of one or moreparameter to be updated.

FIG. 3 depicts spiral graph 300 illustrating the parameter sensitivityof a power system model's prediction in accordance with embodiments.Spiral graph 300 is a visualization of both the magnitude and dependencypredictions of power system model 146 sensitivity to parameters. Inaccordance with embodiments, the values on the vertices of a spiral canbe arranged in such a way that the magnitude of sensitivity decreases ina counter-clockwise direction from the origin point (0) of the graphicalspiral. The spiral graph also provides interconnections 305 between anyparameters having an interdependency in the model's sensitivity to theinterconnected parameters.

The spiral graph is a useful visual tool in selecting those parametersmost identifiable as having an impact on the model's prediction. Forexample, visual analysis of the spiral graph in FIG. 3 shows thatparameters P8, P5 are the most identifiable parameters because they havehigh sensitivity magnitudes and low sensitivity dependency. Althoughparameter P9 indicates that the power model has a greater magnitudesensitivity to parameter P9 than parameter P5, parameter P9 has a muchgreater sensitivity dependence—indicated by the six interconnectionsbetween parameter P9 and parameters P12, P1, P11, P18, P16, P7, where nosensitivity dependency is indicated for parameter P5. Similarly,although parameters P17, P6, P4 have no sensitivity dependency, themodel's magnitude sensitivity to these parameters is lower than itsmagnitude sensitivity to parameters P5, P9.

FIG. 4 depicts spiral graph 400 illustrating the parameter sensitivityof a power system model's active power prediction in accordance withembodiments. FIG. 5 depicts spiral graph 500 illustrating the parametersensitivity of a power system model's reactive power prediction inaccordance with embodiments. Each spiral graph 400, 500 is avisualization of both power system model 146 parameter magnitudesensitivity (shown by a parameter's distance from origin (0,0) on thespiral graph) and parameter dependency sensitivity (shown by the numberof interconnections 405, 505 between parameters).

Embodying systems and methods utilize actual disturbance data monitoredby PMUs coupled to the electrical distribution grid. Therefore, powergeneration systems need not be taken off-line to evaluate the powersystem model. Accordingly, embodiments provide a non-invasive solutionwithout any interruption of grid operations. Additionally, sinceembodiments leverage disturbance data across multiple events, there is ahigh probability of success in ensuring a good match between powersystem model prediction output and measurements across a range ofevents.

In accordance with embodiments, a set of identifiable parameters can befound, where the calculation of dependency is not limited to between thetop two well-conditioned parameters, but rather a dependency among allselected model parameters can be calculated. This calculation ofdependency is implemented using the null space instead of a distancebetween trajectory sensitivities. Embodying approaches provide acomprehensive parameter identifiability (magnitude sensitivity anddependency sensitivity) assessment across multiple events instead ofonly one event.

In accordance with some embodiments, a computer program applicationstored in non-volatile memory or computer-readable medium (e.g.,register memory, processor cache, RAM, ROM, hard drive, flash memory, CDROM, magnetic media, etc.) may include code or executable instructionsthat when executed may instruct and/or cause a controller or processorto perform a method of identifying the magnitude and dependency ofdevice parameter sensitivities in a power system model by using dataobtained from PMUs monitoring multiple disturbance events, as disclosedabove.

The computer-readable medium may be a non-transitory computer-readablemedia including all forms and types of memory and all computer-readablemedia except for a transitory, propagating signal. In oneimplementation, the non-volatile memory or computer-readable medium maybe external memory.

Although specific hardware and methods have been described herein, notethat any number of other configurations may be provided in accordancewith embodiments of the invention. Thus, while there have been shown,described, and pointed out fundamental novel features of the invention,it will be understood that various omissions, substitutions, and changesin the form and details of the illustrated embodiments, and in theiroperation, may be made by those skilled in the art without departingfrom the spirit and scope of the invention. Substitutions of elementsfrom one embodiment to another are also fully intended and contemplated.The invention is defined solely with regard to the claims appendedhereto, and equivalents of the recitations therein.

We claim:
 1. A system comprising: a server including a control processor; the server in communication with a data store, the data store including one or more records containing phasor measurement unit monitored data representing a response of a power system to multiple disturbance events; a model calibration unit configured to provide event screening, simulation of a power system model response to the multiple disturbance events, and simultaneous tuning of a power system model; the data store including executable instructions that cause the control processor to: instruct the model calibration unit to perform a simulation using default model parameters in the power system model; perform a parameter identifiability analysis which identifies, for each of a plurality of parameters across the multiple disturbance events, a magnitude of sensitivity of a parameter to change and a sensitivity dependency of the parameter with respective to other parameter sensitivities; generate a spiral graph comprising a spiral visualization in which the plurality of parameters are plotted based on a magnitude of sensitivity on a first axis and dependency sensitivity on a second axis; select a set of parameters from the plurality of parameters based on positions of the set of parameters plotted on the spiral graph; and update the default model parameters based on the selected set of parameters to cause the power system model to generate a more accurate prediction of a reaction of the power system to a disturbance event.
 2. The system of claim 1, the default model parameters including model parameters stored in model parameter records prior to performance of the simulation.
 3. The system of claim 1, the parameter identifiability analysis including a sensitivity study to determine the power system model magnitude sensitivity and dependency sensitivity to the plurality of parameters.
 4. The system of claim 3, the sensitivity study including conducting a simulation by varying values of each of the plurality of parameters and measuring a difference in the simulated performance to a performance of the power system model based on default parameter values.
 5. The system of claim 1, the executable instructions configured to cause the control processor to generate at least one of estimated parameter values, confidence metrics, and graphical images of model error response versus measured data.
 6. The system of claim 1, the parameter identifiability analysis applying at least one of unscented Kalman filtering and optimization-based parameter estimation.
 7. A method comprising: receiving monitored data representing a response of a power system to multiple disturbance events; instructing a model calibration unit to perform a simulation using default model parameters in a power system model; performing a parameter identifiability analysis which identifies, for each of a plurality of parameters across the multiple disturbance events, a magnitude of sensitivity of a parameter to change and a sensitivity dependency of the parameter with respective to other parameter sensitivities; generating a spiral graph comprising a spiral visualization in which the plurality of parameters are plotted based on a magnitude of sensitivity on a first axis and dependency sensitivity on a second axis; selecting a set of parameters from the plurality of parameters based on positions of the set of parameters plotted on the spiral graph; updating the default model parameters based on the selected set of parameters to cause the power system model to generate a more accurate prediction of a reaction of the power system to a disturbance event.
 8. The method of claim 7, the default model parameters including model parameters stored in model parameter records prior to performance of the simulation.
 9. The method of claim 7, the parameter identifiability analysis including a sensitivity study to determine the power system model magnitude sensitivity and dependency sensitivity to the plurality of parameters.
 10. The method of claim 9, the sensitivity study including conducting a simulation by varying values of each of the plurality of parameters and measuring a difference in the simulated performance to a performance of the power system model based on default parameter values.
 11. The method of claim 7, including generating at least one of estimated parameter values, confidence metrics, and graphical images of model error response versus measured data.
 12. The method of claim 7, the parameter identifiability analysis including applying at least one of unscented Kalman filtering and optimization-based parameter estimation.
 13. A non-transitory computer readable medium having stored thereon instructions which when executed by a control processor cause the control processor to perform a method comprising: receiving monitored data representing a response of a power system to multiple disturbance events; instructing a model calibration unit to perform a simulation using default model parameters in a power system model; performing a parameter identifiability analysis which identifies, for each of a plurality of parameters across the multiple disturbance events, a magnitude of sensitivity of a parameter to change and a sensitivity dependency of the parameter with respective to other parameter sensitivities; generating a spiral graph comprising a spiral visualization in which the plurality of parameters are plotted based on a magnitude of sensitivity on a first axis and dependency sensitivity on a second axis; selecting a set of parameters from the plurality of parameters based on positions of the set of parameters plotted on the spiral graph; updating the default model parameters based on the selected set of parameters to cause the power system model to generate a more accurate prediction of a reaction of the power system to a disturbance event.
 14. The non-transitory computer-readable medium of claim 13, wherein the method further comprises storing the default model parameters prior to performance of the simulation.
 15. The non-transitory computer-readable medium of claim 13, wherein the performing comprises performing a sensitivity study to determine the power system model magnitude sensitivity and dependency sensitivity to the plurality of parameters.
 16. The non-transitory computer-readable medium of claim 15, wherein the sensitivity study includes conducting a simulation by varying values of each of the plurality of parameters and measuring a difference in the simulated performance to a performance of the power system model based on default parameter values.
 17. The non-transitory computer-readable medium of claim 13, wherein the method further includes generating at least one of estimated parameter values, confidence metrics, and graphical images of model error response versus measured data. 